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2009, 2009(Special): 1-10. doi: 10.3934/proc.2009.2009.1

Energy solutions of the Cauchy-Neumann problem for porous medium equations

Goro Akagi 1,

1. 

Department of Machinery and Control Systems, College of Systems Engineering and Science,, Shibaura Institute of Technology, 307 Fukasaku, Minuma-ku, Saitama-shi, Saitama 337-8570

Received  August 2008 Revised  February 2009 Published  September 2009

The existence of energy solutions to the Cauchy-Neumann problem for the porous medium equation of the form $v_t - \Delta (|v|^{m-2}v) = \alpha v$ with $m \geq 2$ and $\alpha \in \mathbb{R}$ is proved, by reducing the equation to an evolution equation involving two subdifferential operators and exploiting subdifferential calculus recently developed by the author.
Keywords: subdifferential operator, Neumann boundary condition, doubly nonlinear evolution equation, Porous medium equation, reflexive Banach space.
Mathematics Subject Classification: 35K65, 35K55; Secondary: 47J35.
Citation: Goro Akagi. Energy solutions of the Cauchy-Neumann problem for porous medium equations. Conference Publications, 2009, 2009 (Special) : 1-10. doi: 10.3934/proc.2009.2009.1
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